If GODS (Indra, Varuna, Yama, Kubera) lived in heaven, how come asuras lived on earth?
I understand that Vishnu and Shiva assumed different forms and came down to earth.
But then, shouldn't asuras assume different forms rather than coming down on earth as Asuras themselves?
Also, if asuras come down to earth without form and live on earth, why GODS (Indra, Varuna, Yama, Kubera) lived in heaven and never lived on earth?
Interesting question but let me clear one point first - NOT all Asuras live on earth, in fact the residence of most Asuras is the underworld. The Shatapatha Brahmana 1.2.4 tells us the reason why they do not live in the same place:
The gods and the Asuras, both of them sprung from Pragâpati,were contending for superiority. The gods vanquished the Asuras; and yet these afterwards harassed them again.
The gods then said: 'We do, no doubt, vanquish the Asuras, but nevertheless they afterwards again harass us. How then can we vanquish them so that we need not fight them again?'
Agni then said: 'By fleeing northwards they escape from us.' By fleeing northwards they had indeed escaped from them.
Agni said: 'I will go round to the northern side, and you will then shut them in from here; and whilst shutting them in, we will put them down by these (three) worlds; and from what fourth world there is beyond these (three) they will not be able to rise again.'
Agni thereupon went round to the northern side; and they (the other gods) shut them in from here; and whilst shutting them in, they put them down with these(three)worlds; and from what fourth world there is beyond these (three) they did not rise again. Now this same (expulsion of the Asuras) is virtually the same act as the flinging away of the grass-bush
The Devi Bhagwat Puran Book 8 Chapter 19 gives the account of the lower lokas that are the residences of various Asura species.
The Atala is where Danavs live, in Vitala it is the Daityas, in Sutala lives Maharaj Bali and his followers, Talatala is the abode of Maya Danav and his kin and in Rasatal live Daityas, Dânavas and Pani Asuras.
Secondly, coming to the gods, the 33 gods mentioned in Shatpatha Brahman 5.1.2 handle different spheres of existence and are broadly divided into three sets - ones who rule earth, second who rule the skies and third who rule the heavens. So we see a few on earth while the rest all remain out of sight! There are many gods who did make Earth their home:
Even if he lives in Patal as Keshav said, Varun lived in the ocean when Rama incarnated as is evident from the episode of him requesting Shri Rama to make a bridge of stones.
Agni lives in the homes of people - he is the messenger as well as the witness of the gods for all Vedic ceremonies.
Dattatreya lived on earth all the time.
Bhumi is the goddess of earth who is supporting all of us.
Ganga is a river-goddess who came down to earth from the heavens.
Shiva & Parvati live on Mount Kailash which is on the planet again. Kartikeya is believed to live in the southern part of India and we have never really heard of him going to any other Loka.
Goddess Durga is known as Vindhyavasini which means she lives in the Vindhya mountains - this implies at least one form of her exists on the earth.
Third, Asuras DO COME to Earth in other forms as well just like gods. For example, Kauravs, Kamsa, Jarasandh etc. were actually Asuras but they appeared as humans. SECTION LXVII of Sambhava Parva lists all the incarnations of gods as well as demons and no one even knew their truth most of the time!
The first of Danavas, who was known by the name of Viprachitti, became that bull among men, noted as Jarasandha. And, O king, that son of Diti, who was known as Hiranyakasipu, was known in this world among men as the powerful Sisupala. He who had been known as Samhlada, the younger brother of Prahlada, became among men the famous Salya, that bull amongst Valhikas. The spirited Anuhlada who had been the youngest became noted in the world as Dhrishtaketu. And, O king, that son of Diti who had been known as Sivi became on earth the famous monarch Druma. And he who was known as the great Asura Vashkala became on earth the great Bhagadatta. The five great Asuras gifted with great energy, Ayahsira, Aswasira, the spirited Aysanku, Gaganamurdhan, and Vegavat, were all born in the royal line of Kekaya and all became great monarchs. That other Asura of mighty energy who was known by the name of Ketumat became on earth the monarch Amitaujas of terrible deeds. That great Asura who was known as Swarbhanu became on earth the monarch Ugrasena of fierce deeds. That great Asura who was known as Aswa became on earth the monarch Asoka of exceeding energy and invincible in battle. And, O king, the younger brother of Aswa who was known as Aswapati, a son of Diti, became on earth the mighty monarch Hardikya.
The great and fortunate Asura who was known as Vrishaparvan became noted on earth as king Dirghaprajna. And, O king, the younger brother of Vrishaparvan who was known by the name of Ajaka became noted on earth as king Salwa. The powerful and mighty Asura who was known as Aswagriva became noted on earth as king Rochamana. And, O king, the Asura who was known as Sukshma, endued with great intelligence and whose achievements also were great, became on earth the famous king Vrihadratha. And that first of Asuras who was known by the name of Tuhunda, became noted on earth as the monarch, Senavindu. That Asura of great strength who was known as Ishupa became the monarch Nagnajita of famous prowess. The great Asura who was known as Ekachakra became noted on earth as Pritivindhya. The great Asura Virupaksha capable of displaying various modes of fight became noted on earth as king Chitravarman.
The first of Danavas, the heroic Hara, who humbled the pride of all foes became on earth the famous and fortunate Suvahu. The Asura Suhtra of great energy and the destroyer of foemen, became noted on earth as the fortunate monarch, Munjakesa. That Asura of great intelligence called Nikumbha, who was never vanquished in battle was born on earth as king Devadhipa, the first among monarchs. That great Asura known amongst the sons of Diti by the name of Sarabha became on earth the royal sage called Paurava. And, O king, the great Asura of exceeding energy, the fortunate Kupatha, was born on earth as the famous monarch Suparswa. The great Asura, O king, who was called Kratha, was born on earth as the royal sage Parvateya of form resplendent like a golden mountain. He amongst the Asura who was known as Salabha the second, became on earth the monarch Prahlada in the country of the Valhikas. The foremost, among the sons of Diti known by the name of Chandra and handsome as the lord of the stars himself, became on earth noted as Chandravarman, the king of the Kamvojas. That bull amongst the Danavas who was known by the name of Arka became on earth, O king, the royal sage Rishika. That best of Asuras who was known as Mritapa became on earth, O best of kings, the monarch, Pascimanupaka. That great Asura of surpassing energy known as Garishtha became noted on earth as king Drumasena. The great Asura who was known as Mayura became noted on earth as the monarch Viswa. He who was the younger brother of Mayura and called Suparna became noted on earth as the monarch, Kalakirti. The mighty Asura who was known as Chandrahantri became on earth the royal sage Sunaka. The great Asura who was called Chandravinasana became noted on earth as the monarch, Janaki. That bull amongst the Danavas, O prince of the Kuru race, who was called Dhirghajihva, became noted on earth as Kasiraja.
The Graha who was brought forth by Sinhika (Rahu) and who persecuted the Sun and the Moon became noted on earth as the monarch Kratha. The eldest of the four sons of Danayu, who was known by the name of Vikshara, became known on earth the spirited monarch, Vasumitra. The second brother of Vikshara, the great Asura, was born on earth as the king of the country, called Pandya. That best of Asuras who was known by the name of Valina became on earth the monarch *Paundramatsyaka**. And, O king, that great Asura who was known as Vritra became on earth the royal sage known by the name of Manimat. That Asura who was the younger brother of Vritra and known as Krodhahantri became noted on earth as king Danda. That other Asura who was known by the name Krodhavardhana became noted on earth as the monarch, Dandadhara.
And, O king, from the tribe of Asuras called Krodhavasa, of whom I have already spoken to thee, were born many heroic kings on earth. Madraka, and Karnaveshta, Siddhartha, and also Kitaka; Suvira, and Suvahu, and Mahavira, and also Valhika, Kratha, Vichitra, Suratha, and the handsome king Nila; and Chiravasa, and Bhumipala; and Dantavakra, and he who was called Durjaya; that tiger amongst kings named Rukmi; and king Janamejaya, Ashada, and Vayuvega, and also Bhuritejas; Ekalavya, and Sumitra, Vatadhana, and also Gomukha; the tribe of kings called the Karushakas, and also Khemadhurti; Srutayu, and Udvaha, and also Vrihatsena; Kshema, Ugratirtha, the king of the Kalingas; and Matimat, and he was known as king Iswara; these first of kings were all born of the Asura class called Krodhavasa. There was also born on earth a mighty Asura known amongst the Danavas by the name of Kalanemi, endued with great strength, of grand achievements, and blessed with a large share of prosperity. He became the mighty son of Ugrasena and was known on earth by the name of Kansa.
The evil-minded and wicked king Duryodhana, the destroyer of the fair fame of the Kurus, was born of a portion of Kali on earth. He it was who caused all creatures to be slain and the earth to be wasted; and he it was who fanned the flame of hostility that ultimately consumed all. They who had been the sons of Pulastya (the Rakshasas) were born on earth among men of Duryodhana's brothers, that century of wicked individuals commencing with Duhasasana as their first. And, O bull among the Bharata princes, Durmukha, Duhsaha, and others whose names I do not mention, who always supported Duryodhana (in all his schemes), were, indeed, the sons of Pulastya.
